• Corpus ID: 184488209

Abelian tropical covers

@article{Len2019AbelianTC,
  title={Abelian tropical covers},
  author={Yoav Len and Martin Ulirsch and Dmitry Zakharov},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}

• Yoav Len, Martin Ulirsch, D. Zakharov
• Published 10 June 2019
• Mathematics
• arXiv: Algebraic Geometry

The goal of this article is to classify unramified covers of a fixed tropical base curve $\Gamma$ with an action of a finite abelian group G that preserves and acts transitively on the fibers of the cover. We introduce the notion of dilated cohomology groups for a tropical curve $\Gamma$, which generalize simplicial cohomology groups of $\Gamma$ with coefficients in G by allowing nontrivial stabilizers at vertices and edges. We show that G-covers of $\Gamma$ with a given collection of stabilizers are in natural bijection with the elements of the corresponding first dilated cohomology group of $\Gamma$.